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  • Open Access

Resummation of Universal Tails in Gravitational Waveforms

Mikhail M. Ivanov1,2,*, Yue-Zhou Li3,†, Julio Parra-Martinez4,‡, and Zihan Zhou3,§

  • *Contact author: ivanov99@mit.edu
  • †Contact author: liyuezhou@princeton.edu
  • ‡Contact author: julio@ihes.fr
  • §Contact author: zihanz@princeton.edu
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Phys. Rev. Lett. 135, 141401 – Published 30 September, 2025

DOI: https://doi.org/10.1103/jzd1-qzkt

Abstract

We present a formula for the universal anomalous scaling of the multipole moments of a generic gravitating source in classical general relativity. We derive this formula in two independent ways using effective field theory methods. First, we use the absorption of low-frequency gravitational waves by a black hole to identify the total multipole scaling dimension as the renormalized angular momentum of black hole perturbation theory. More generally, we show that the anomalous dimension is determined by phase shifts of gravitational waves elastically scattering off generic source multipole moments, which reproduces the renormalized angular momentum in the particular case of black holes. The effective field theory approach thus clarifies the role of the renormalized angular momentum in the multipole expansion. The universality of the point particle effective description of compact gravitating systems further allows us to extract the universal part of the anomalous dimension, which is the same for any object, including black holes, neutron stars, and binary systems. As an application, we propose a novel resummation of the universal short-distance logarithms (“tails”) in the gravitational waveform of binary systems, which may improve the modeling of signals from current and future gravitational wave experiments.

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Phys. Rev. Lett. 135, 141401– Published 30 September, 2025
  • Received 8 May 2025
  • Accepted 5 September 2025
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